Efficient conservative ADER schemes based on WENO reconstruction and space-time predictor in primitive variables

Table 8 Initial states left (L) and right (R) for the Riemann problems for the Baer-Nunziato equations

	\(\boldsymbol{\rho}_{\boldsymbol{s}}\)	\(\boldsymbol{u}_{\boldsymbol{s}}\)	\(\boldsymbol{p}_{\boldsymbol{s}}\)	\(\boldsymbol{\rho}_{\boldsymbol{g}}\)	\(\boldsymbol{u}_{\boldsymbol{g}}\)	\(\boldsymbol{p}_{\boldsymbol{g}}\)	\(\boldsymbol{\phi}_{\boldsymbol{s}}\)	\(\boldsymbol{t}_{\boldsymbol{e}}\)
BNRP1 (Deledicque and Papalexandris 2007): \(\gamma_{s} = 1.4\), \(\pi_{s} = 0\), \(\gamma _{g} = 1.4\), \(\pi_{g} = 0\)
L	1.0	0.0	1.0	0.5	0.0	1.0	0.4	0.10
R	2.0	0.0	2.0	1.5	0.0	2.0	0.8
BNRP2 (Deledicque and Papalexandris 2007): \(\gamma_{s} = 3.0\), \(\pi_{s} = 100\), \(\gamma_{g} = 1.4\), \(\pi_{g} = 0\)
L	800.0	0.0	500.0	1.5	0.0	2.0	0.4	0.10
R	1,000.0	0.0	600.0	1.0	0.0	1.0	0.3
BNRP3 (Deledicque and Papalexandris 2007): \(\gamma_{s} = 1.4\), \(\pi_{s} = 0\), \(\gamma _{g} = 1.4\), \(\pi_{g} = 0\)
L	1.0	0.9	2.5	1.0	0.0	1.0	0.9	0.10
R	1.0	0.0	1.0	1.2	1.0	2.0	0.2
BNRP5 (Schwendeman et al. 2006): \(\gamma_{s} = 1.4\), \(\pi_{s} = 0\), \(\gamma _{g} = 1.4\), \(\pi_{g} = 0\)
L	1.0	0.0	1.0	0.2	0.0	0.3	0.8	0.20
R	1.0	0.0	1.0	1.0	0.0	1.0	0.3
BNRP6 (Andrianov and Warnecke 2004): \(\gamma_{s} = 1.4\), \(\pi_{s} = 0\), \(\gamma _{g} = 1.4\), \(\pi_{g} = 0\)
L	0.2068	1.4166	0.0416	0.5806	1.5833	1.375	0.1	0.10
R	2.2263	0.9366	6.0	0.4890	−0.70138	0.986	0.2

Values for \(\gamma_{i}\), \(\pi_{i}\) and the final time \(t_{e}\) are also reported.